In Sections 7 and 8 we provide a formal semantics for the numeric extension and temporal extension of PDDL2.1. Together these sections contain 20 definitions. The lengthy treatment is necessary because the semantics we have developed adds four significant extensions over classical planning and the semantics Lifschitz developed for STRIPS [LifschitzLifschitz1986]. These are:
The structure of the definitions is as follows. Definitions 1 to 15, given in Section 7, define what it means for a plan to be valid when the plan consists of only non-durative actions. Definitions 1 to 6 set up the basic terminology, the foundational structures and the framework for handling conditional effects and primitive numeric expressions. Definition 2 meets the first requirement identified above, defining states. Definition 9 meets the second requirement, defining when a goal description is satisfied in a state. Definition 11 defines a simple plan, extending the classical notion of a sequence of actions by adding time. Definitions 12 meets the fourth requirement, by defining when two actions cannot be executed concurrently. Definition 13 meets the third requirement, defining what we mean by execution of actions, including concurrent execution of actions. Definitions 14 and 15 define the execution of a plan and what it means for a plan to be valid, given the basis laid in the previous definitions.
In Section 8 the semantics is extended to give meaning to durative actions. We begin with Definition 16, which defines ground durative actions analogously to Definition 6 for simple (that is, non-durative) actions. Similarly, Definition 17 parallels the definition of a simple plan (Definition 11) and Definitions 19 and 20 parallel those for the execution and validity of simple plans (Definitions 14 and 15). Definition 18 is the critical definition for the semantics of plans with durative actions, supplying a transformation of temporal plans into simple plans, whose validity according to the semantics of purely simple plans, can be used to determine the validity of the original temporally structured plans.